Seasonal Surface Temperatures of Dark Earth

The Visible Paleo-Earth (VPE) project provides a unique set of data about the evolution of Earth in the last 750 million years that can be used not only to study Earth's past biospheres but also to understand Earth-like exoplanets. Before studying exoplanets, we want to understand first past and present Earth as a basis for comparisons. Here we are presenting the basic analysis necessary to reconstruct the mean and seasonal global surface temperature of past and present Earth, and important factor in determining the evolution of Earth's habitability.

The mean global surface temperature for land and oceans today is about 14°C (20th Century value from NOAA). This is controlled by a bond albedo of 0.306 and a greenhouse warming of 33°C. Mean global seasonal temperatures oscillate between 12° and 16°C, a seasonal change of just 4°C caused by variations in the insolation from the distribution of landmasses and oceans, and the axial tilt.

We want to determine the absolute maximum seasonal temperature change that a very Earth-like planet can experience (assuming today's continental configurations, obliquity, and atmosphere) We considered a Dark Earth (Fig. 1), an Earth with bright landmasses (albedo = 1) but dark oceans (albedo = 0), and no clouds. Earth will be darker and hotter with such conditions, but it will also show wider seasonal temperature changes. The effects of clouds will make the planet colder and also reduce seasonal variations.

A model of our Dark Earth was run for a full year simulation time. We measured the visual geometric albedo, of the Sun-faced side (a constant phase angle of zero), as the ratio of the integrated density of the planet frame with respect to a white Lambert sphere (Fig. 1). For simplicity, we assumed a constant conversion factor ab = 0.834ag between the bond albedo ab and the visible geometric albedo ag derived from values for Earth today (ab = 0.306 and ag = 0.367, ref). The surface temperature was calculated from the equilibrium temperature and a current greenhouse warming of 33°C.

Figure 1. These are a few sample frames of a simulation of a Dark Earth planet with bright landmasses (albedo = 1) and dark oceans (albedo = 0). This configuration provides the highest contrast ratio between landmasses and oceans. The frames show a white Lambert sphere (used for calibration), landmasses at equinox, at vernal solstice, and winter solstice, respectively. A complete animation with all the frames for a full year (8760 frames in about 6 minutes) is available here.

Our results show that our Dark Earth has a bond albedo of 0.288 and a mean global surface temperature of 21°C. There is a 10°C maximum change in surface temperatures between seasons (Fig. 2). Therefore, we conclude that 10°C is the absolute maximum change in seasonal surface temperatures that can experience Earth today independently of ocean color, vegetation, ice or cloud covers. The effects of clouds will reduce this number, but a different distributions of landmasses or obliquity can increase it.

Figure 2. Mean monthly global surface temperature for our Dark Earth model (red) as compared to Earth today (blue). The Dark Earth temperatures are not only higher and wider but also out of phase with current cycles. The mean annual global surface temperature for Dark Earth is 21°C (today 14°C) with a variation of 10°C (today 4°C).

We will later add dynamic clouds to our Dark Earth, and finally use and fit the full terrestrial model of today from the VPE, until we calibrate and reproduce the current Earth surface temperatures (blue line in Fig. 2). Once we do that, we will be able to extend the analysis to model the mean monthly global surface temperatures of Earth in the last 750 million years. The models will also consider variations in solar luminosity, Earth's obliquity, cloud cover, and greenhouse effects. Our results will be validated with other proxies of global paleotemperatures. Then, we will explore the same approach with hypothetical computer generated Earth-like exoplanets using Monte Carlo methods. For instance, Earth's past landmasses only oscillated between 10 to 30% global coverage and we need to test exoplanets with larger land areas.